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Sunday, April 9, 2017

The problem of Hume’s problem of induction

In the
context of discussion of Hume’s famous “problem of induction,” induction is
typically characterized as reasoning from what we have observed to what we have
not observed. For example, we reason
inductively in this sense when we infer from the fact that bread has nourished
us in the past that it will also nourish us in the future. (There are, of course, other ways to
characterize induction, but we can ignore them for the purposes of this post.)

Hume asks
how we can be rationally justified in reasoning this way, and his answer is
that we cannot be. For there are, he
says, only two sorts of purported justifications that could be given, and
neither of them works. The first would
justify induction in terms of what Hume calls the “relations of ideas.” The proposition that all bachelors are unmarried is a stock example of something true by
virtue of the relations of ideas. It is
a necessary truth insofar as the idea of being a bachelor logically entails the
idea of being unmarried. Justifying
induction in these terms would involve showing, for example, that there is a
similar logical relationship, and thus a necessary connection, between the idea
of bread and the idea of being nourishing to us.

But there
is, Hume argues, no such connection. For
it is at least conceivable that bread
could fail to nourish us, in a way it is not conceivable that a bachelor could
be married. In general, it is
conceivable with respect to any cause
that its usual effect might fail to follow upon it. Hence we cannot reason on the basis of the
relations of ideas to the conclusion that causes that we have not observed will
operate like those we have observed.

The other
way induction might purportedly be justified would be in terms of “matters of
fact.” The proposition that many bachelors go to singles bars is
true, not because the idea of being a bachelor logically entails the idea of
going to a singles bar, but rather because it simply happens to be a contingent
empirical fact that many bachelors do this.
To justify induction in terms of “matters of fact” would involve arguing
that as a matter of contingent empirical fact, induction has been a reliable
way of reasoning, so that we have grounds to trust it in the future.

But the
trouble with this attempt to justify induction is that it is circular. To infer from the fact that many observed
bachelors have gone to singles bars the conclusion that many unobserved bachelors will do so too
presupposes the reliability of induction.
To infer from the fact that induction has been reliable in observed
cases the conclusion that it will be reliable in future cases also presupposes
the reliability of induction – where its reliability is, in this case, exactly
what such an argument is supposed to be showing.

In summary,
Hume’s argument against the possibility of justifying induction goes as
follows:

1. Induction
could be rationally justified only in terms of either the relations of ideas or
matters of fact.

2. But it
cannot be justified in terms of the relations of ideas, since for any cause and
any effect it is conceivable that the one could in the future exist without the
other.

3. And it
cannot be justified in terms of matters of fact, since such a purported
justification would presuppose the reliability of induction and thus beg the
question.

4. So
induction cannot be rationally justified.

As David
Stove once said of Plato’s Theory of Forms, the sequel to Hume’s argument has
been centuries of rapturous applause among philosophers. Stove didn’t mean it as a compliment; he was
mocking something he took to be overrated.
The mockery is in my view not justified in Plato’s case, but it would
have been justified had the barb been directed instead at Hume’s overrated
argument. For what we have here is one
of many instances of Hume’s application of general philosophical presuppositions
which we know to be highly problematic at best and demonstrably false at
worst.

First, the
initial premise of Hume’s argument is an application of Hume’s Fork, the
principle that all knowable propositions concern either relations of ideas or
matters of fact. But Hume’s Fork – which
is itself neither true by virtue of the relations of its constituent ideas, nor
true by virtue of empirically ascertainable facts – is notoriously
self-refuting. It is as metaphysical a
principle as any Hume was trying to undermine with it, and its very
promulgation presupposes that there is a third epistemic point of view
additional to the two Hume was willing to recognize. In that case, though, Hume’s celebrated
“problem of induction” cannot even get out of the starting gate. Its entire force depends on a dichotomy that
is demonstrably false.

Nor can the
Humean plausibly salvage the argument by softening Hume’s Fork so as to avoid
the self-refutation problem. For the
softening can take one of three forms.
The Humean could liberalize the principle by admitting that there is
after all a third category in addition to “relations of ideas” and “matters of
fact”; or he could maintain this dichotomy while liberalizing the notion of
“relations of ideas” in such a way that Hume’s Fork itself will come out true
by virtue of the relations of ideas; or he could maintain the dichotomy while
liberalizing the notion of “matters of fact” in such a way that Hume’s Fork
will come out true by virtue of matters of fact.

Whether and
how any of these strategies could be developed in a plausible way is another
question. But the point for present
purposes is that, however that might go, if
he is going to salvage Hume’s problem of induction, the Humean will have to
soften Hume’s Fork in such a way that it will vindicate Hume’ Fork itself without also vindicating induction at
the same time. In particular, the Humean
will have to acknowledge a third category of knowable propositions in addition
to relations of ideas and matters of fact while
at the same time showing that induction isn’t justifiable in terms of this
third category. Or he will have to
liberalize the notion of “relations of ideas” while at the same time showing that induction isn’t justifiable in
terms of this new, liberalized notion.
Or he will have to liberalize the notion of matters of fact while at the same time showing that induction
isn’t justifiable in terms of that
new, liberalized notion.

Good luck
with all that. Until one of these
strategies is actually developed, we don’t really have a Humean “problem of
induction.”

That’s just
one problem. Another is that Hume’s
second premise depends on the principle that conceivability is a guide to real
possibility. Now, contemporary
philosophers never tire of pointing out how problematic this principle is when
Cartesians deploy it in arguments for their brand of dualism. The Cartesian says that we can clearly
conceive, without contradiction, of minds existing in the absence of bodies,
and concludes from this that it is therefore possible in principle for minds to
exist apart from bodies. But how, the
critic responds, can we rule out the possibility that this seems conceivable
only because of a deficiency in our grasp of the mind? Someone with only a vague understanding of
what a Euclidean triangle is might think it possible for such a triangle to
have angles that add up to something other than 180 degrees. When he acquires a better grasp he will
realize that this is not in fact possible.
Perhaps, the critic suggests, a more penetrating grasp of the nature of
the mind would reveal that it cannot really exist apart from matter.

But the same
sort of objection can be raised against Hume (and, in my view, with greater
justice). Perhaps if we had a complete
grasp of the nature of bread and the nature of the human body, we would see
that it is not in fact possible for
bread to fail to be nourishing to us. If
so, then we would be justified in
judging that bread will nourish us in the future just as it has in the past.

Now, the
reason Hume is so confident that this is not the case is because of what
commentators call his copy principle,
viz. the thesis that an idea is just a faint copy of an impression. I have an impression
of red when I am looking at a certain apple.
When the apple is not present I can call to mind what that color looked
like, and this mental image is (Hume claims) my idea of red. More complex
ideas are made up of combinations of simpler ones of this sort. My idea of bread, for example, is just a
combination of the idea of a certain color, the idea of a certain shape, the
idea of a certain texture, and so forth.
Thus understood, it seems plausible to say that there is nothing in my
idea of bread that entails that it will be nourishing in all cases.

But this
account of our ideas is ludicrous. It
reflects the imagist thesis that a concept is essentially a kind of mental
image, and imagism is demonstrably false.
We have a great many concepts that are clearly not identifiable with
mental images. For example, the concept
of triangularity is not identifiable
with any mental image. Any triangle you
can imagine will always be of a certain specific color – black, red, green, or
whatever – whereas the concept triangularity
applies to all triangles whatever their color.
Any triangle you can imagine will be a right triangle, or an equilateral
triangle, or in some other way have features that don’t apply to all triangles,
whereas the concept triangularity does
apply to all triangles. And so
forth. This is just the
beginning ofthe
problems with imagism. (Here’s a fun
exercise: Try to identify the mental
image that the concept mental image
might be identified with.)

Then there
is the assumption that all necessity is logical
necessity, viz. the sort of necessity exhibited by the relations between
concepts. Aristotelians and other non-Humean
philosophers would deny this. They hold
that there is a deeper, metaphysical kind of necessity that exists in things themselves and not merely in our
concepts of things. Logical necessity,
on this view, is an echo of this deeper sort of necessity. And the echo might not ring out very strongly
in a mind that has too superficial an acquaintance with all the relevant facts.
Hence, suppose that, given the nature of
bread and given the nature of a healthy human body, it cannot possibly be the
case that bread will fail to nourish such a body. It may still turn out that a given person
might conceive of a scenario wherein bread fails to be nourishing, not because such
a failure is really possible, but rather merely because that person’s intellect
has not attained a sufficiently penetrating grasp of the natures of bread and
of the body.

For the
non-Humean, then, it is simply not the case that all propositions are either necessary but mere conceptual truths (“relations
of ideas”), or empirical but merely
contingent truths (“matters of fact”).
There are also truths which are empirical
but nevertheless necessary. That bread will nourish the body could be a
necessary truth even if we can know that it is true (if it is in fact true) only
by empirical investigation of the natures of bread and of the body.

Naturally,
the Humean will disagree with all of this, but the point is that, unless he
offers an independent argument against these alternative ways of understanding
the nature of concepts, necessary truth, etc., he will not have given us any
non-question-begging reason to believe that there is a “problem of induction.”

The real
problem, then, is not the problem of justifying induction. The real problem is justifying the claim that
there is a “problem of induction” that remains once we have put aside the false
or otherwise problematic philosophical assumptions that Hume himself deployed
when arguing that induction cannot be justified.

It seems that this post, rather than dissolving the problem of induction, merely reframes it: the way a thing behaves might be necessary given its essence, but how can we ever be certain that we have a true grasp of a thing's essence? Maybe it is part of bread's essence to cease being nourishing at exactly 1:33pm tomorrow, and we simply don't know it yet. The core of the problem doesn't seem to go away.

The main point of this post is that the assumptions Hume employed to justify his argument fail.

The problem of induction states that we cannot justifiably infer from past observations, future events. But Hume's reasoning is dubious.

Now, if we can adequately discern the essence of a particular thing, then we will know how the thing will act. If we know a thing's essence, we just know how it will act.

How we can ever be certain we have a true grasp of a thing's essence? That itself is another topic. Either way, that is no problem of induction.

So suppose we do not know the essence of the bread and thus don't know it will cease being nourishing at 1:33pm tomorrow - that is no problem of induction, but merely a failure to grasp a thing's essence adequately.

How is not a problem of induction? It certainly concerns the question of whether we can predict unobserved events from observed ones. The problem remains, because we can never know whether our past observations of a thing's behavior were enough to achieve a sufficiently veridical understanding of that thing's essence to accurately predict its future behavior.

But if this is the argument, you've conceded Jason's point -- you have actually moved to a different problem. The objection is that we can't be sure we know what things are in the first place, which, if so, would be something true at present, regardless of any questions about the past and future, and would have nothing to do with induction except as a precondition. It's true that we can't have induction if we can't figure out what things are, but this is not the problem of induction.

Anon:"We can never know whether our past observations of a thing's behavior were enough to achieve a sufficiently veridical understanding of that thing's essence to accurately predict its future behavior."

I think you're smuggling back in Hume's problem, as if "understanding a thing's essence" just is observing past behavior.

But if the intellect can grasp being, if --as Feser is asserting-- the intellect can in principle discover the necessary connections between cause and effect that inhere in a thing's nature, then it can in principle understand an essence enough to know bread won't suddenly stop nourishing at 1:33pm tomorrow.

Whether or not the mind is able to discover those connections, is another topic.

The problem of induction *does* plague anyone who holds to modern popular philosophies, I think -- scientism, naturalism, etc. Feser here refutes the problem, but only by changing philosophical assumptions (implicitly) from those ones, no? So it's not so clear if this is a refutation of the problem of induction, or a use of the PoI to refute various Humean philosophies.

There is an other, and much more important problem with induction: you can never be sure you are right. You can't tell if what's true for your sample size of n will hold for all reality. Eg. you've only ever seen white swans and discover that black ones exist in Australia (cf Nassim Taleb). Or you're a turkey and assume that since you were fed yesterday, you will be fed today, but it's Thanksgiving day. Or, if before 2007 you assumed that house price will continue to go up since they have been without stop since 1975...

Messrs Baum and Callahan, the problem I pointed out is indeed not Hume's. But it is an epistemological problem nonetheless, and it is different from a "problem of arithmetic". Arithmetic is deductive, and hence its conclusions are certain if the there are no mistakes in reasoning from arithmetic principles. But induction, on which the natural sciences - and arguments which go from cause to effect - are based, is different. Here we argue from individual observation to general conclusion and even if no logical mistakes are made, we cannot arrive at an absolutely certain conclusion, as in maths.

I wonder how to understand the certainty in the correctness of the conclusions of arguments for God's existence. Prof Feser, is metaphysical inductive reasoning different from scientific inductive reasoning?

Hume's poor epistemology notwithstanding, the problem of induction is real, and most philosophers would agree that attempts to solve it have failed, whatever they may think of Hume. I've written more about the problem of induction here.

But to me, the real question is: can scientists justify the legitimacy of inductive inferences regarding the future or about hitherto unobserved places, without making any reference to God, as the Ultimate Ground of things' intelligibility? I would argue that they can't.

Anonymous is right: "the way a thing behaves might be necessary given its essence, but how can we ever be certain that we have a true grasp of a thing's essence?" And I would add: in the absence of God, how can we be certain that a thing's essential properties are space- and time-independent? Remember: there are infinitely many ways in which hitherto-exceptionless regularities can fail to hold in the future. And what about grue?

However, the problem disappears if we two fairly minimal assumptions about God: first, that if God were to create a cosmos, God would want to produce intelligent beings; and second, that God would want these intelligent beings to know that their Creator exists.

Given these assumptions, the skeptical problem disappears: if God wants to be known by us, then the things in the world must behave in a reliable fashion. And if they do, then of course, human beings can go about their daily lives and scientists can conduct their research without having to continually worry about whether the sky will fall on them, as the ancient Gauls did. But if I were an atheist, I would be just as worried as the Gauls were.

These assumptions seem to follow naturally from the traditional, classical conception of God as a Being Whose nature it is to know and love in a perfect and unlimited way, and Whose mode of acting is simply to know, love and choose (without anything more basic underlying these acts). Such an essentially intelligent (and loving) Being might well wish to create beings capable of knowing (and loving) their Creator.

"It may still turn out that a given person might conceive of a scenario wherein bread fails to be nourishing, not because such a failure is really possible, but rather merely because that person’s intellect has not attained a sufficiently penetrating grasp of the natures of bread and of the body"

I wonder if Hume's Fork is self-refuting. My guess is that Hume would call it a matter of fact, and so not true by definition but only the most probable truth we have to go on. I think I could finagle a Humean argument that made it a relation of ideas, but to do so is very un-Hume. If you challenged the fork, the response would probably just be to come up with some truth that couldn't be described by it, and dos standard of proof would be met if you failed to come up with one after thinking while.

The fork-as-matter-of-fact would be justified after failing to come up with a counter example after thinking a while? Isn't that a form of induction? "The fork has described all true propositions up until now"... But induction itself is undermined by the fork.

Hume wouldn't grant this, though. Even if we concede that matters of fact involve repeated experiences, Hume account is that this gives rise to nothing more than an expectation on the part of the perceiver, not an insight into what nature is like. The Fork is itself just an expectation we form about things and not an insight into what the mind is like. Hume explicitly rules out any such insight into the mind when he defends his nominalism.

My own account of Hume starts by being puzzled by the skepticism he has for causes in part one of the Treatise compared to the enthusiasm he has for them in part 2. One account is that he wants to humanize reason, and he recognizes on some level that understanding nature is a divine prerogative. Think of Kant's Critique starting with a claim about human reason.

If I understand it correctly, and perhaps to make some things explicit, the very classification of all propositions into two and only two classes, viz., either those based on "relations of ideas" or those based on "matters of fact" requires a conceptual justification or an empirical justification. The latter case is a non-starter because any empirical justification about there being two and only two classes of propositions would presuppose induction. Therefore, the former is the only possible means, though it does not admit or appear to admit any justification that shows that it is necessarily the case that only conceptual or empirical propositions exist. Furthermore, the proposition central to Hume's Fork -- "there are two and only two kinds of propositions, etc..." -- must itself fall on one of the fork's two prongs. Clearly, it cannot be an empirical proposition because it does not concern anything contingent and would presuppose induction. Therefore, it would need to be a conceptual proposition. However, the proposition does not yield any "self-justification". Therefore, it is neither and Hume's Fork is self-refuting.

I saw this yesterday, and while I greatly respect Dr Craig, I was quite disappointed in Craig for his terse remark.

As Dr Feser and others have demonstrated, Aquinas's first 2 ways are easily presented as metaphysical arguments, and they in no way rely on physics or cosmology, outdated or otherwise.

Many people falsely assume that the the arguments are physical and outdated, and many more are unaware of the metaphysical articulations.

Also, perhaps Dr Craig regards Aquinas's original articulation as physical and thus false; but perhaps accepts the subsequent contemporary articulations that are in purely metaphysical terms. This all said, I think the first two ways are metaphysical (not physical) arguments in their original context in any case.

Rest easy; the first and second ways are very viable metaphysical arguments, and so presented, do not rest on old cosmology.

Off topic or not it is well worth considering. WLC was responding to a reader who worried that many, if not all, the more sophisticated proofs of God require those in the discussion to first build, adopt, or otherwise become familiar with an entire metaphysical system prior to beginning any argumentation. Both the reader and WLC are worried that this prevents ordinary people (whoever they are) from really engaging with the problem of God. WLC maintains that the proofs he puts forward are set up in such a way that an entirely new (or old) system is not necessary before beginning.

The principle of induction is a principle of epistemology. A principle of epistemology says how we should reason. One can only reason about a subject matter that has some order. To reason about something that has some order entails using the principle of induction. - It is not possible to reason about order without assuming the principle of induction.

Perhaps I should explain what “order” means. Order characterizes those sets of data that are such that knowing part of them it is possible to predict the other part with better than chance success. Or, in other words, order characterizes set of data of low Kolmogorov complexity. A big part of reasoning has the end to attain that power of prediction (perhaps all reasoning; can the reader think of a counterexample?). For example to have reasoned that 5 plus 5 equals 10, gives one the power to predict that if one puts 5 beans and 5 beans together, should one count the resulting heap one would arrive to 10. But the very end of attaining the power of prediction entails the assumption that order will hold, or in other words is based on the assumption that the principle of induction is true (in the sense that it will lead to true beliefs, of pragmatically useful beliefs). One cannot reason without assuming that the principle of induction is true.

In fact I wonder how Hume reasoned without assuming that principle. Take for example his reasoning about the principle of induction as explained in the OP. It rests on the premise of “Hume's Fork”. Assume that this principle was true in Hume's time and thus that Hume did well in using it. Without the principle of induction why should the philosopher believe that this principle is still true today? Why assume that between his time and now reality hasn't changed in a way that invalidates Hume's Fork? Or take one or the other prongs of the Fork. Hume thinks that one can know a proposition by the relations of ideas. Suppose that reality is such that this principle is true at one instant. Absent the principle of induction why believe it will true in the next? Perhaps in between reality has changed in a way that falsifies it. And what about the other prong, namely that of observing matters of fact? Well our knowledge of matters of fact is based on our *remembering* certain observations. Absent the principle of induction why believe that our memory is reliable?

The idea I am trying to express here is that without the principle of induction there is no reasoning. But then the principle of induction is necessarily true. To say “I am reasoning” entails saying “I am using the principle of induction”.

This is certainly not true. There are plenty of ordered sets that can be successfuly predicted with some algorithm other than an inductive one; if the set has sufficiently anti-inductive properties (which it could while still having low Kolmogorov complexity), then one would have to use some such other algorithm.

It solves nothing to define reasoning as "using induction." That just pushes the question back to: is reasoning useful (or reliable) in finding truth and making predictions? If not, who cares about reason?

“There are plenty of ordered sets that can be successfuly predicted with some algorithm other than an inductive one”

I didn't explain myself well. But since you raised the issue of algorithms, let me point out that the very concept of algorithm entails that it is reasonable to expect that the algorithm will work every time it's executed, or in other words entails the principle of induction.

My point is that the principle of induction is as basic as reason itself; to ask for an argument for induction is like asking for an argument for reason. Or to ask somebody “Show me why the use of words is useful.” It's one of this cases that asking a question is the answer.

Perhaps I can restate my argument thus:

1. The purpose of reasoning is to find useful truths.2. There are no useful truths unless the principle of induction holds.3. Therefore there is no reasoning unless the principle of induction holds.

Incidentally the principle of induction is not “If P holds for some Xs then it holds for all Xs”, but “If P holds for some Xs then, unless one has a defeater, it is reasonable to hold that P holds for all Xs”. I say without that principle there is no reasoning whatsoever.

Finally in the previous comment I used the concept of order because in all cases where order exists the principle of induction holds.

”It solves nothing to define reasoning as "using induction."”

I am not defining reason in this way. I am claiming that all reason (as we normally use the concept) entails the principle of induction perhaps as an unstated assumption. If you disagree, can you offer a counterexample?

”That just pushes the question back to: is reasoning useful (or reliable) in finding truth and making predictions? If not, who cares about reason?”

Can I offer a counterexample to the claim that all reasoning uses the principle of induction? Yes. If the ZF axioms are true, then the sum of the squares of the lengths of the short sides of a right triangle is the same as the square of the length of the hypotenuse. That follows from reasoning, and does not depend on the principle of induction.

Now on to your main argument:

"1. The purpose of reasoning is to find useful truths."

Actually, the purpose of reasoning is to find truths, full stop. But for the purpose of argument, let's allow this one.

"2. There are no useful truths unless the principle of induction holds."

That's not correct.

Let's take the following proposition: "Today, unlike all prior days, jumping in front of a bus is necessary for the continuance of life, as opposed to inconsistent therewith."

If this is true, then it is certainly useful. And for a Humean, it's just as likely to be true as the opposite, "inductive" conclusion (at least qua reasoning). In fact, all states of affairs are equally likely, or at least equally rationally believable. Consequently, absolutely any course of action can be viewed as equally justifiable with respect to reason. The course of action suggested by induction is not rationally favored. Suppose, for example, that I choose to believe that the above statement about buses is correct, but only today (and then will never be correct again). If I'm right, then that will have been a very useful truth, although not obtained by induction.

Now, it's true that any algorithm I might choose -- for example, the one that tells me to jump in front of a bus today, but not yesterday and not tomorrow -- will, if I run it long enough, come to be inductively favored. The problem is that "long enough" here essentially means infinitely long; because for any finite amount of evidence, it will not be at all favored over any other algorithm. (This can be formalized in the context of Kolmogorov information and Solomonoff induction; informally, it's basically a manifestation of the grue problem or of Hume's problem, depending which side you look at it from).

So there are two ways of stating the problem with your claim. First: you're wrong. There can be reasoning using any of an infinite number of algorithms that could give uniformly correct answers, any of which (for a Humean) is equally likely to give correct answers. Or second: you're right, there is no reasoning unless a principle of induction holds. But there is no "the" principle of induction; there are infinitely many, and they're incompatible, with nothing to suggest a way to choose between them.

“That follows from reasoning, and does not depend on the principle of induction.”

We wouldn't know any geometrical truths if shapes did not keep their properties. But to assume that, is to assume the principle of induction. Now one could retort that mathematical objects exist outside of time and thus cannot change their properties, but this philosophical view is grounded on the fact that shapes, countable things, etc. do not in our experience change their properties from moment to moment, and, again, to assume that this will keep holding is to assume the principle of induction. One could insist that independently from experience we clearly see, in our mind's eye as it were, that mathematical objects do not change their properties. It's inconceivable that they do. But even though we can discuss the reasonableness of the principle “conceivability implies possibility” it is certainly not reasonable to hold that “inconceivability implies impossibility”. Our confidence in the immutability of ideal forms was forged in a reality in which the principle of induction is true, and wouldn't otherwise.

“Actually, the purpose of reasoning is to find truths, full stop.”

There is delightful short story by Stanislaw Lem about this: Two inventor engineers visit a planet ruled by a philosopher king who above all values truths. So he offers the engineers a great deal of money if they would construct a machine that would continuously print out truths. They construct the machine, sign all the guarantee papers, collect their fee, and secretly leave the planet before daybreak. The reason for their escape becomes clear when the king tries out the machine. It works exactly as it should printing at great speed only truths. But they are all useless truths such as “This morning Mrs Brown's hen laid an egg with three brown spots on it.”

My premise was “The purpose of reasoning was to find useful truths”. Since in the set of all truths the vast proportion is next to absolutely useless, it should be obvious that the purpose of reasoning is indeed to find useful truths. Indeed the more useful ones. It would be unreasonable for somebody to reason about questions the true answer of which has much less usefulness than many others.

“That's not correct. Let's take the following proposition: "Today, unlike all prior days, jumping in front of a bus is necessary for the continuance of life, as opposed to inconsistent therewith."”

Well, it is striking that of all the actual truths we know you had to device a hypothetical one to counter my second premise. This speaks volumes *for* that premise. But suppose there are a few useful truths for which the principle of induction need not hold. What would follow? It would only follow that in some rare cases knowledge can be useful even if the principle of induction does hold in their case, and thus need not be assumed when reasoning about them.

Having said the above I do not understand your hypothetical example well enough to respond. Do you mean that today the laws of nature changed in a way that I should jump in front of a bus? If that's what you mean then you are begging the question since today the laws of nature haven't in fact changed. Philosophy is a practical business. We are discussing reason in the actual reality.

“And for a Humean, it's just as likely to be true as the opposite, "inductive" conclusion (at least qua reasoning).”

I am not sure I understand you correctly, but perhaps the thought here is as follows: Truth is about actual reality. We know that in actual reality a lot of things change, but there are many things that appear not to change, including, for example, the particular way many things in reality change. The property of reality of containing many things that do not change allows us to produce useful knowledge. But we don't really *know for certain* that the things that appear immutable (the “universals”) night not change. We don't know for certain, because the only things we know for certain is current experience and nothing else. So suppose we are wrong; suppose tomorrow something we hold to be immutable does change. Suppose the very foundational structure of reality would change. What then? Shouldn't we in philosophy take into account *that* possibility?

My answer is, no we shouldn't. Life is short and we have lot of important work to do with reality as it seems to be, to worry about realities which would seem differently. Reason guides us in how we should distribute our efforts too.

Interestingly enough Hume's doubt makes more sense on theism. On theism all created reality (all there is except what's metaphysical ultimate in God; including inconceivably, the properties of mathematical objects) might change from its very foundations up, and will change if God so deems to be good. Thus the theist might have some reason to speculate about this. But even at these rarefied heights the principle of induction holds vis-a-vis the immutable metaphysical ultimate nature in God (and our reasoning will depend on our knowledge about that nature). It really seems there is no reasoning without the principle of induction. Reason requires some ground to stand.

It must be I who am being unclear. You make reference to the fact that my counter-inductive hypotheses are counterfactual, and to the fact that the ordinary laws of physics worked today, as if it's some kind of victory. It's not, because I have not been arguing that induction actually *isn't* reliable. Of course it is. I'm arguing that a Humean has no rational warrant for using it. For a Humean, no matter how many times the laws of physics are the same, it's no reason to believe they will be TOMORROW, or are ABOUT to be TODAY.

Your story by Stanislaw Lem isn't really relevant. Yes, it's silly if we decide to use our ability to reason to come to truths that nobody would care about. But if reason is not a tool for finding out the truth about anything at all, then it's not even a good tool for finding out about useful things.

Next: you totally dodge the point of the bus example. You say that my example shows only that there might be some cases where the principle of induction doesn't apply, and we just don't have to use induction about those cases. The point is, for the Humean, EVERY case is like that beforehand. There is no warrant for considering future induction to be probably reliable at all. Therefore, there is no rational reason not to step out in front of the bus (but please don't -- you'll die), or to believe that it will kill you. You say "philosophy is a practical business," as if that is some kind of answer. Getting from the premise "Philosophy is a practical business" to "We should use induction" has a missing premise: "Using induction is practical." For a Humean, that's a premise that can not be established. Of course, it's true. But the argument is very powerful in quite a few popular belief systems, and so the fact that people holding them continue to view the use of induction as practical merely shows that they are too practical to actually put their claimed belief system into practice, and that it arguably isn't their belief system at all.

Oh, and incidentally, your argument about induction being needed for mathematical reasoning is completely wrong, as well.

A triangle, as treated in mathematics, is a *completely* abstract object. It's true that our definition of it was originally motivated by our experiencing triangles in the real world. But a triangle at this point is perfectly abstractly defined. All the triangles in the world could turn into wavy ellipses tomorrow, and it wouldn't change a dang thing about the properties of triangles. It might just mean that none of them existed in our actual world. Euclidean geometry would all still be true no matter what happened to the universe tomorrow; it just might not be applicable to our universe (even as much as it is now).I invite you to go read a mathematical proof and show me just what part of it depends on inductive reasoning (in the sense used here).

“your argument about induction being needed for mathematical reasoning is completely wrong”

I am happy you bring that up, for I think the case of mathematical truths can help us clarify what we are talking about.

“A triangle, as treated in mathematics, is a *completely* abstract object. It's true that our definition of it was originally motivated by our experiencing triangles in the real world. But a triangle at this point is perfectly abstractly defined.”

Perfectly defined, yes. But even then our understanding of the abstract triangle cannot be separated from the particular experiences that led us to it. You cannot cut the umbilical cord between the abstraction and the particulars it is derived from. Now it is true that once defined as a formal system the whole of Euclidean geometry could by developed by an intellect which has never experienced anything like shapes (imagine a world with intellects which only experience sounds; they will have the particular experience of counting and thus will understand algebra, but not of shapes). No matter how advanced geometry that intellect would do by using our formal system, it would never understand what a triangle is – indeed would not have the slightest idea. Notwithstanding the fact that it would know a great many sophisticated theorems about triangles. Don't you agree?

(I would appreciate an answer here. I have recently had a discussion with a participant in this blog who insisted that Berkeley denied the possibility of abstract knowledge. But it is implausible to believe that Berkeley denied the possibility of knowing that 2+2=4. Even without giving any quotes, I think that Berkeley meant what I describe above.)

“Euclidean geometry would all still be true no matter what happened to the universe tomorrow; it just might not be applicable to our universe (even as much as it is now).”

Right, but truth has meaning only when it means something. Any formal system will produce theorems that are true in that system. Separated from particular experiences the meaning of these truths concerns only the game of shifting symbols around following particular rules. Which by the way is perfectly OK. Mastering games has again and again proven to be quite useful.

“I invite you to go read a mathematical proof and show me just what part of it depends on inductive reasoning (in the sense used here).”

All abstract truths can be checked even if only as truths concerning a game of symbols. (If it were in principle impossible to in some way check a mathematical truth, then that truth would be completely irrelevant in our life and thus completely useless.) Now that checking need not be exhaustive – for example we can check the truth about there being an infinite number of prime numbers by picking a few largish numbers and constructing a larger prime.

To answer your question: In math we assume the principle of induction when we assume that next time we check some mathematical truth things will come out as expected. (The same by the way also goes for the truths of logic which we use in mathematical proofs.)

Now I am perfectly aware that it seems inconceivable to us that we might check tomorrow for the truth of the theorem 2+2=4 and find out that it is false (you check that theorem by writing on a piece of paper two dots which symbolize the number 2, then another two dots, and then counting the resulting lot – you should count up to 4). But inconceivability does not imply impossibility. God could give us tomorrow the experience of checking and failing to find that 2+2=4. As could the programmer of our world in the case we live in a computer simulation.

Order exists to the degree that the principle of induction holds. Should the principle of induction fail, that order fails, some truths derived through reasoning about that order fail, and thus the reasoning by which we derived those truths fails.

No, I don't agree that your hypothetical mind would not understand triangles. I agree that it would have a very different sense of them than we have, but it would not completely fail to understand triangles anymore than we completely fail to understand 7-spheres (which are something we've never seen and cannot picture).

It's of course true that we have to believe that reason is universal and unchanging, and that our minds have access to it, in order to do (and believe in) mathematics. That isn't really an inductive result, though: we can't test the universality of reason even today. It is a presupposition of there being any knowledge. But if reason has the properties we suppose, then the theorems of geometry do not depend in any way, shape, or form on the principle of induction (although our own ability to understand them correctly might collapse if our brains started working very differently).

“I have not been arguing that induction actually *isn't* reliable. Of course it is. I'm arguing that a Humean has no rational warrant for using it.”

Right. Actually nobody has a rational warrant for using the principle of induction. So what? Neither do we have a rational warrant for using reason. Epistemology is justified by how well it works, not by its having rational warrant. To ask for rational warrant in the context of epistemology would lead to an infinite regression, wouldn't it?

“But if reason is not a tool for finding out the truth about anything at all, then it's not even a good tool for finding out about useful things.”

As a tool reason serves for finding truths. Still our purpose when using this tool is to find useful truths. My argument was that one can't use reason to find useful truths without assuming the principle of induction. But perhaps there useful truths one cannot find out using reason.

“You say "philosophy is a practical business," as if that is some kind of answer. Getting from the premise "Philosophy is a practical business" to "We should use induction" has a missing premise: "Using induction is practical." For a Humean, that's a premise that can not be established.”

Ah, but it can be established. By definition, what's practical is established by practice. And by our practice in the fields of logic, math, physical sciences – it is established that using induction is practical for a huge range of truths.

“The point is, for the Humean, EVERY case is like that beforehand.”

Right, but is that a reasonable worry? As I have argued, all reasoning is inductive since it requires some ordered ground to stand. Should we worry about things that we cannot reason about?

Actually, on second thoughts perhaps we should. Perhaps through reason we can discover its limits, and that's a useful truth to know. My worry here is not the reasonableness of the principle of induction, but its adequacy.

“but it would not completely fail to understand triangles anymore than we completely fail to understand 7-spheres”

But we can only understand multidimensional spheres because we have the particular experiences of the neighborhood we are talking about. We know what a point is, what a distance is, what a surface is, what multiple dimensions are, and so on. The intellect who did not have any particular experience of shapes would not know what it is talking about. I suppose it's the same question discussed in the argument about Mary living in a black-and-white room. No matter how much abstract knowledge you learn, if you don't experience the particular thing you won't know it.

Actually the question we are discussing may be open to experimental verification. We can formalize euclidean geometry as a set of axioms and production rules so that each theorem is represented by a string of characters. Suppose now we collect a large a large number of theorems about triangles (including perhaps the respective proofs) to somebody and ask her to find out the single digit number that is hidden in all of them. Or even better to an intelligent computer. It is conceivable that they should correctly discover that that digit is three, but I think in reality they won't. I doubt any intelligence, no matter how great, could (unless it had stored a large set of mathematical theorems and used pattern matching to discover the solution, a possibility one could work around by picking not the common triangle but some random mathematical object). I wonder if one could mathematically prove what I assume is true. The point is that if such a representation is not sufficient for abstracting the number 3, surely no intelligence would be able to form the abstract idea of triangle.

”we can't test the universality of reason even today. It is a presupposition of there being any knowledge.”

This sounds close to what I've been saying. For surely a big part of knowledge we get through reason entails the use of induction. The remaining question is whether there is knowledge about any order which does not entail the use of induction. You seem to think that mathematical knowledge is such a case.

I wonder: How do you imagine the world is that would make mathematical truths and physical truths to be different in kind? After all, at first sight finding out truths about math looks similar to finding truths about math – in both cases we use symbolic manipulation, we empirically check results to guide our efforts, we easily communicate such results, and so on. Physics can (and should) be considered as a mathematical problem, namely the problem of discovering mathematical patterns present in the large set of physical phenomena. That after finding such a pattern (say Newton's mechanics) it is always possible to find a better pattern (say general relativity) does not mean anything in particular. Perhaps similarly there are very powerful theorems about Euclidean shapes which we haven't discovered yet. Given gravitational phenomena, Newton's mechanics and general relativity are as much necessary as any mathematical truth. What I am trying to say is really simple: Just consider the entire set of physical phenomena as a mathematical object.

So, to come back to our discussion, the same inductive faith in the immutability of the order present in physical phenomena which underlines discovery in physics, that same inductive faith in the immutability of the order present in formal systems (or symbolic games) underlines discovery in math. To think that the apparently absolute immutability of both realms is accidental in the case of physics but necessary in the case of math only makes sense if one commits oneself to certain metaphysical assumptions, such as the reality of Plato's realm of ideal forms and moreover that the human intellect has direct access to that realm. But, metaphysically speaking, such rather fantastic commitments look more implausible, or weird, or far removed from what we actually know of the human condition – than theism. Why then not embrace theistic metaphysics instead? On theism the order of both mathematical phenomena (in the realm of the experience of counting, or more generally of manipulating symbols on a piece of paper) and of physical phenomena (in the larger realm of interacting with our mechanistically ordered (aka “physical”) environment – they both are grounded on God's creative will and rational mind. Whether “necessary” or “accidental” becomes a non-issue. There, necessarily as far as we are concerned, they are.

“But if reason has the properties we suppose, then the theorems of geometry do not depend in any way, shape, or form on the principle of induction (although our own ability to understand them correctly might collapse if our brains started working very differently).”

At first sight it feels inconceivable that starting tomorrow 2+2=4 will stop checking out. But using Descartes's idea of the evil demiurge, or the more modern hypothesis that we live in a computer simulation (which some naturalists take seriously indeed since the possibility seems to follow from assumptions they have already committed to) – don't you agree that it may be the case that we have been cognitively fooled all along and that 2+2=5?

This will be only a partial reply for now (sorry -- but you posted a lot).

First, you distinguish between the rationality of induction and its adequacy. I can see that that can be a useful distinction. We're being imprecise about our definitions in a sense, but the question I'm interested in is, "Does the Humean have any reason to believe that induction is useful in forming true beliefs?" The answer, I maintain, is no. This remains so if you replace "reason" by "cause," or the entire phrase by "to believe that induction is adequate to form true beliefs?"

You say that we can't find useful truths without using the principle of induction. But that is a separate question from whether we can find useful truths WITH using the principle of induction. If your ONLY basis for using the principle of induction is that without it we can't find useful truths, then that's not really true anymore. There are other fiat assumptions we can make that will yield claims which, if true, will also be useful. For example, my bus example.

You write: "Ah, but [that induction is practical] can be established. By definition, what's practical is established by practice. And by our practice in the fields of logic, math, physical sciences – it is established that using induction is practical for a huge range of truths."

There are two possible relevant definitions for "practical" that I can imagine. One is "what's established by practice." The other is "useful for future practice." The whole problem here is building a bridge between the two. If you want to choose the former definition, then fine -- I'll grant you that induction is practical. But I won't let you equivocate and slip in the other definition, for example by saying that we're interested in "practical truths" only. Why? We're interested in USEFUL truths, but it's no longer clear (for a Humean) that practical and useful are the same. Or if you choose the second definition, then no, what's established by practice is not necessarily practical.

You then allow that the Humean's worry perhaps IS something worth worrying about. Perhaps, then, we agree?

On to your example about multi-dimensional spheres, finding numbers, etc. Here I disagree once again. Mathematicians have found simple unifying numbers characterizing incredibly abstract spaces that bear no virtually no relationship to anything we experience in the world. So in your example, I don't doubt that a sufficiently sophisticated mathematical culture, even if not used to geometry, would eventually find three in triangles.

As for the question of how I find math and physics different: math follows by rational argument from definitions and axioms, and physics does not, but relies as well on observation. We do not know the results of the observations a priori. Pretty easy, right?

Such dialogues help me think. I hope the size of the texts does not hide the simplicity of my position which is that to claim a truth about an order entails the assumption that that order will be there next time one looks. Thus one cannot reason about order without assuming the principle of induction. Any epistemic trouble one may see in this state of affairs is useful only for clarifying what one means by “true belief” or by “I believe in”.

“the question I'm interested in is, "Does the Humean have any reason to believe that induction is useful in forming true beliefs?" The answer, I maintain, is no.”

Consider the absurdity the Humean's position when he says the following: “I take this medicine because I believe that it is more probable that it will cure me than kill me. That medicine was made on the assumption that scientific beliefs are true. The truth of scientific beliefs is based on the principle of induction. I have no reason to believe that induction is useful in forming true beliefs. Thus I have no reason to believe that the medicine I am taking will more probably cure me than kill me. Nevertheless I take the medicine.”

“You say that we can't find useful truths without using the principle of induction”

No, I say that we can't find useful truths *about order* without using the principle of induction.

The error I find in Hume's reasoning is not about his fork being self-refuting. (I have serious doubts about self-refutation being a valid tool when reasoning about epistemology.) The error I find is that he misreads a basic fact of the human condition, and thus about the relevance of one branch of his fork. So empirical facts – facts we know by direct and immediate experience without the need for any reasoning – are not only the deliverances of the senses about the environment we find ourselves in, but also facts about the huge range of the qualities of our experience of life. Our experience of beauty, of the moral good, of justice, of freedom, of love, of desire – are all empirical facts. So is our experience of rationality, and in it of the reasonableness of the principle of induction. I claim that the truth of the principle of induction is an empirical fact and is thus entirely accounted for by Hume's fork.

Feser discusses this idea in the OP but I think commits the same error when he speaks it entails a circular inference. I say it's not an inference at all. A fact of the human condition – a direct and immediate experience present in the human condition – is the visual-like sense of the reasonableness of induction. Now all our experiences may lead to error, and often do lead to error. Rationality proceed by assuming that all the factual deliverances of our experience of life are how they seem, and correcting particular beliefs only when there is reason to do so. The alternative position that rationality proceeds by carefully justifying each belief not only leads to infinite regressions but also to much waste of time. I have the impression that the success of formal systems as tools for discovering truths has misled many a philosopher to fixate only on mechanistic ways of epistemology and also on mechanistic metaphysical views. It's seems to me a wonder to see philosophers who live in a place mainly of qualitative facts focusing mainly on the far less significant quantitative facts.

Given the above, shouldn't we worry about perhaps finding reasons that defeat any empirical seeming? Shouldn't we actively search for such reasons? Yes, indeed we should, and it is excellent practice to try to find defeaters for one's own beliefs. But the Humean is *not* searching for positive reasons to doubt the principle of induction (indeed has not offered the slightest such reason), but instead argues that there is no reason to trust in it. Thus, the Humean takes the unreasonable alternative epistemic path I discussed above, namely to think that truth (including epistemological truth) must built from the ground up by supporting each truth on other truths. There is a chicken-and-egg kind of problem between epistemology and metaphysics, but I think it is probable that Hume's naturalistic metaphysical commitments (basically that reality is a mechanism), has pushed him into serious epistemological error.

Finally I have earlier argued for the principle of induction not because I hold that such argument is necessary but in order to show how to doubt in the principle of induction is to doubt in all reasoning about order. The thrust of my argument is to show that it is virtually certain that we will never really find any defeater for the principle of induction, and thus that in this case it is not wise to invest one's time in trying to find such a defeater.

“There are two possible relevant definitions for "practical" that I can imagine. One is "what's established by practice." The other is "useful for future practice.”

I dislike the philosophical fashion of making distinctions within distinctions of concepts. I say words have a common meaning: that of the folk. If when thinking about that meaning the philosopher finds it lacking for her purpose the reasonable thing to do is to coin an new word defining its meaning the way she needs. Trying to maintain a connection to the original word is entirely superfluous and may easily lead to confusion. Words have a way to move philosophers, like the tail wagging the dog (a great example here is the concept of “compatibilist freedom”). So, to come back to our subject matter, “practical” in the folk sense entails “relevant for the future”. So when one observes that philosophy is a practical business one means it's useful for our future life.

“Perhaps, then, we agree?”

I kind of hope we don't :-) Discussions tend to be much more fruitful when characterized by disagreement. In our current discussion I feel I have greatly profited from our disagreement. I sometimes have the sense that the deepest truths are such that one embraces them moved by value judgments. Thus in a dialogue agreement should not always be expected, even under the best circumstances.

“So in your example, I don't doubt that a sufficiently sophisticated mathematical culture, even if not used to geometry, would eventually find three in triangles.”

Interesting that you should feel so certain. I feel quite certain for the opposite, but do have my doubts. The interesting thing here is that it might be possible to experimentally resolve our disagreement. Whereas the question of the knowledge of colors analyzed in Frank Jackson's argument does not appear to be thus amenable. Given that my claim about the impossibility of knowledge concerns a quantitative matter it is a much stronger one than his. Should my claim be proven experimentally then we'd have strong reason to believe that qualitative knowledge such as the experience of color is impossible at the absence of particular experience.

“As for the question of how I find math and physics different: math follows by rational argument from definitions and axioms, and physics does not, but relies as well on observation.”

I find that's a remarkably interesting issue. I think I can make a very strong case that physics is a sub-field of math. God willing I will post some thoughts about this later.

I don't have much time to continue this discussion, alas. Only let me point out that I wasn't introducing a new definition of practical. I was pointing out that YOU are equivocating by using two radically different definitions of "practical" and then assuming them to be the same at a key step in your argument.

As to the rest, I should perhaps re-emphasize that I'm not arguing that Hume's argument is successful against induction, full stop; it's not. I'm arguing that it's successful against induction *for anybody who shares his metaphysical assumptions,* or a wide range of similar assumptions. You keep saying things that make it unclear to me that you actually disagree with this. If you say that Hume is led to his position by his erroneous metaphysical assumptions, for example, then you're in essence saying that, for somebody with those metaphysical assumptions, his argument works, which is what I have myself been maintaining.

I do think induction can be justified if one is willing to adopt a significantly thicker metaphysics, such as theism or even Christian theism (which I am). But that doesn't mean Hume's arguments aren't devastating to a materialist.

@timocrates, a Humean doesn't have the resources for a rich definition of "bus" or the like. Anarchy is all he has. So while you're right that it's radically anarchistic, anarchy is what Humeanism entails. Which is the point.

It's a bit of an odd argument. The reason why we have distinctions like analytic/synthetic, a posteriori/a priori, and necessary/contingent the inadequacy of the Humean dichotomy. Precisely one way to read what Kant was doing is to read him as showing that dichotomies like Hume's were getting their plausibility wholly from the fact that they were conflating very different distinctions. If Hume were right, we wouldn't need analytic/synthetic, necessary/contingent, a priori/a posteriori; they'd be otiose.

You're argument also is playing a bit fast and loose with the distinctions themselves. Kant's analytic/synthetic distinction is analytic -- it's purely a distinction of logical structure of judgments (in a subject-and-predicate judgement in which A is predicated of B, A is either conceptually contained in B or it is not). Later bastardizations conflating this with true-in-virtue-of-linguistic-meaning and true-by-virtue-of-extralingual-correspondence require taking the original distinction and conflating it with a different distinction about sentences, one that is very definitely synthetic in Kant's sense, since it requires relating sentences to something other than sentences. Thus its self-refutation would not be at all surprising; it treats two logically different kinds of distinctions as if they were the same. Similar things can be said about the other distinctions mentioned: it's a necessary truth that truths are either necessary or not necessary, for instance, and if one gets any other result, it's a sign that more than one distinction is being muddled.

And it's a bit baffling why you think a criterion's being self-refuting is just fine; if a criterion applies to itself in a self-refuting way, it proves itself false. If you have a claim saying that all claims are only either A or B, but that claim is itself neither A nor B, then we know the claim is false. So why would we still be treating it as a criterion?

Hume's distinction between 'matters of fact' and 'relations of ideas' may be inadequate in many ways, but its inadequacy is not established in Feser's argument for self-refutation. You are welcome to believe it has been replaced with more appropriate concepts, as many do, perhaps.

Our available categories, furthermore, seem appropriate, though not isomorphic: one speaks of possibility, the other of meaning or truth-makers, another of knowledge, and so on.

Furthermore, I specified that my focus was on more recent formulations, hence I spoke of analyicity and synthecity in terms of meaning, and how it seems perfectly serviceable to understand this within a meta-language M referring to the categories within an object language L.

Lastly, I note that what is at issue is the appearance of self-refutation is not sufficient, for Carnap's criterion is not self-refuting, although it appears to be so, if one confuses these speech-acts within a meta-language M with speech-acts occurring within the object-language L.

(1) Self-refutation in and of itself would establish inadequacy; this is elementary logic. It's exactly one of the ways you establish the inadequacy of a general principle.

(2) Carnap's distinction, despite the usual name, is not a general criterion for meaning; its application is wholly relative to the given linguistic framework with which you are already working. Any given linguistic framework will always have sentences not covered by the distinction (namely, those outside the given framework), and therefore that particular application will not apply to them at all; and, what is more, what counts as falling on one side of the division will depend on how the framework is set up -- and therefore something 'analytic' given one language framework (say, a K system of modal logic) will not be, given another (say, standard propositional logic). Thus there is not a single distinction here, but a schema for infinitely many different language-relative distinctions. Carnap's distinction works to the extent it does precisely because it is impossible for it to work as a general criterion; it does not pre-establish what can count, and when it is used what counts as analytic or synthetic can only be determined by investigation of the linguistic framework in each particular case.

(3) You have not established that the appearance of self-refutation is mere appearance of self-refutation, in the case actually discussed in the post.

(4) For that matter, the post does not even address Carnap. If you like Carnap's distinction, stop conflating it with Hume's distinction; the latter is not even the same kind of distinction devoted to the same kind of analysis. The only things they have in common are two prongs, and there is no reason to think that what is true of one will generally be true of the other.

To address your first, second and fourth points, yes, I acknowledge this, and explained why prima facie cases of self-refutation are not necessarily cases of self-refutation (e.g. Carnap's criterion). This is the 'fourth way' available that doesn't let in a principle of induction through the window.

If one were adverse to adopting a Carnapian approach, Georges Dicker's 'Hume's Epistemology and Metaphysics: An Introduction' provides a different route to address the problem of self-refutation raised by Feser, which is why I mentioned it in my post.

Furthermore, I did not conflate Carnap's and Hume's distinctions; I made their differences quite clear, and noted that it was a companion in guilt argument.

On your third point, you may disagree, but at this juncture, the ball is in Feser's court to show that either the avenue taken by Dicker in defence of Hume's Fork or a Carnapian 'fourth way' are impermissible responses to Feser's objection.

It is late here and I must be going to bed. Speak soon, if you wish to continue speaking further.

Furthermore, I did not conflate Carnap's and Hume's distinctions; I made their differences quite clear, and noted that it was a companion in guilt argument.

Nonsense. There is no companionship in guilt; this is precisely the conflation (which you go on blatantly to make again by pretending that a Carnapian 'fourth way' could be a "response" to an objection against a completely different distinction that is used for a completely different kind of analysis in a completely different kind of inquiry. A Carnapian 'fourth way' is an impermissible response, because it logically cannot address an objection to the Humean distinction. They aren't even in the same logical family; the one does not address the issues of the other.

It is not nonsense, since I mention in the post that it is a companion in guilt argument. I also mention in the post that I believe Feser may have thought the argument for self-refutation was plausible, since it is a philosophical myth that it was effective against Ayer's criterion, then went on to show that this belief that it was an effective criticism is doubtful on the logical empiricist's terms, viz. Carnap's meta-philosophical programme effectively addresses this criticism.

Nathan, are you aware that there a number of assumptions built into the claimed distinction variously listed as analytic vs synthetic or matters of fact.

As an example, it is very obvious that a child of 4 can have a clear idea of a cone. Later, the child can be taught truths about conic sections, such as asymptotes of hyperbolae, which can be said to be "included in" the child-of-4's concept of cone only in a way that relies on lots and lots of additional claims that are hotly debated and not at all obviously true. More importantly, the "included in" almost certainly cannot be adequately accounted as a linguistic feature.

The whole underpinning of the treatment (by Hume, and later attempts to fix his problems) assumes things about epistemology that are not necessarily true, and if his assumptions don't pan out his whole approach is undermined.

(1) Your claim that you are not conflating is nonsense; the companionship in guilt argument is a made-up fiction in your head that ignores identifiable logical differences between the distinctions that are immediately relevant (e.g., the fact that the language/meta-language distinction has no possible analogue for Hume's distinction) and pretends that they logically work in similar ways when they manifestly do not. The relationship between the two is not adequate for any kind of argument of the sort that you are trying to make; nor have you done anything but lazy hand-waving to back your assertions that it is.

In fact, the two logically cannot be conflated for exactly the reasons I indicated: they are differently structured as distinctions, they are used for different kinds of analysis, and they are drawn in completely different kinds of inquiry, all of which are essential in assessing distinctions, and therefore what is true of one cannot be carried over without proof to the other; Carnap's distinction is relativized and Hume's can't be; Carnap's distinction is confined to language and Hume's must be completely general; and so forth.

(2) As everyone can read, Ed's argument does not in any way appeal to Ayer or to Carnap; nor does it claim at any point to be dealing with anyone but Hume. It is you, and you alone, who are generalizing it.

Ah, at last a comment about the photo. As someone living in Scotland I have to ask why that particular photo of a Scotsman was used. I haven't actually come across many (any?) Scotsmen who look like that. I think the person who posed for the photograph must be one of those Americans who like to parade their Scottish ancestry. Come to think of it you are much more likely to find people looking like that in the USA than in Scotland.

So because we know that not always some things will produce their usual effect we reason as a rule to not expect of necessity things to occur of necessity that are not necessary: but certainly we did not come to this conclusion by experience and induction.

This is the sort of thing that could not be said by anyone with serious exposure to either scholastic metaphysics or criticisms of it; since it adapts its approach to the topic, and draws on a massive legacy of philosophical concepts, it has literally been regularly attacked for not being neat and tidy for the past three or four centuries at least.

Karl Popper's point is that "induction is not logic" is well taken. However, inductive inference, particularly in the Bayesian sense, is a workhorse of our modern scientific world. The "problem of induction" is solved by what we really do, which is an iterative process of codification of observed regular behavior into laws and law-like descriptions, theorizing to explain/predict the valid domain of laws, allowing us to penetrate deeper into the phenomena and structure of the world.

Great post. I think Ayn Rand (bless her) actually encapsulated the decisive point for me for the first time (and woke me out of my Humean slumbers) when she talked simply and clearly about things having natures, therefore their causal properties being necessary features of them. Whatever else one might think of her, surely she was a good Aristotelian insofar as she stuck to that insight.

It follows, then, that induction is "simple", as Aristotle said (or was it "easy"?). Things have natures, essences, and you try to encapsulate them in definitions, if the thing is the type of thing you think it is, then it must necessarily behave the way it does and have the effects it does - that's actually what necessity is, the necessity contained in things in the world, and the logical necessity found in logic/language is derived from that, from the necessity found in the world; this as opposed to what modern philosophy developed, which is the odd idea that logic is just shuffling beans around according to rules, with consistency in the application of the rules for bean-shuffling being the only "necessity", and the "interpretation" of the symbol system being arbitrary. How much evil has that (as one might call it) autistic view caused (via its connection to scepticism and eventually nihilism)! Hecatombs and abbatoirs, all from a silly mistake.

The trick is of course identifying the essence correctly.

The problem with Hume was that for all his brilliance and incisiveness, he was tenaciously attached to the "Way of Ideas" (as Reid called it - i.e. the tradition stemming ultimately from Descartes, through Locke and Berkeley to Hume). If you think of experience as some kind of detachable (potentially standalone) entity in itself, that isn't intrinsically (at least partly) evidence of the external world, then you've opened the door to global scepticism right off the bat, and the ineluctable outcome is, again, autistic solipsism and its bean-shuffling view of logic, with all the various forms of phenomenalism and idealism being merely desperate rearguard actions, unstable equilibria on the way to that.

About Me

I am a writer and philosopher living in Los Angeles. I teach philosophy at Pasadena City College. My primary academic research interests are in the philosophy of mind, moral and political philosophy, and philosophy of religion. I also write on politics, from a conservative point of view; and on religion, from a traditional Roman Catholic perspective.